Question

Verify whether the statement $q\vee [p\vee (\sim q\left)\right]$ is a tautology or a contradiction.

Answer 1

We have to verify whether the statement $q\vee [p\vee (\sim q\left)\right]$ is a tautology or a contradiction.

Let us construct the truth table for $q\vee [p\vee (\sim q\left)\right]$

$p$	$q$	$\sim q$	$p\vee (\sim q)$	$q\vee [p\vee (\sim q\left)\right]$
$T$	$T$	$F$	$T$	$T$
$T$	$F$	$T$	$T$	$T$
$F$	$T$	$F$	$F$	$T$
$F$	$F$	$T$	$T$	$T$

The last column contains only $T^{\prime }s$.

Therefore $q\vee [p\vee (\sim q\left)\right]$ is a tautology.